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Is New York City Mayor Michael Bloomberg really thinking of running for President next year as a self-financed independent? Or is he lowering his sights, as one Big Apple tabloid reported last week, and planning to take aim at the Albany statehouse in 2010 instead?

"Did Mike Bloomberg become a multi-billionaire by lowering his sights? I don't think so," says a friend of the popular second-term mayor. "Why would he want to be governor? If he runs for anything, it'll be the White House."

Sources close to the mayor confirm that Bloomberg is not interested in trying to oust newly elected Democratic governor Eliot Spitzer from his job. "He's become the Paris Hilton of politics  people love to speculate about him," says one source, who adds that Bloomberg, a nominal Republican, is preparing to throw himself into the presidential race next spring, if he sees an opening. He's told people privately that he'd be willing to spend $500 million or more to finance an independent, third-party presidential campaign  to collect the signatures needed to get him on the ballot in all 50 states, to buy ads and to pay for staff.

Given the pace at which the leading candidates in the two parties are raising vast sums of money, however, half a billion might not cut it. Of course, Bloomberg, the 65-year-old founder of Bloomberg L.P., has plenty more cash if he needs it. He spent a combined $160 million of his own money to win the mayor's job in 2001 and re-election 2005. But he's a pragmatic man. He may have billions to spare, but he didn't get that rich by pursuing fantasies that had no chance of panning out.

Kevin Sheekey, the mayor's political adviser, says Bloomberg might run if the two parties put forward nominees that play to their base constituencies but turn off the center of the electorate. "It's not impossible that that window could open and he could run a viable campaign," Sheekey says with careful deliberation. "And if it opens, he should consider it."

For now, Bloomberg is spending a conspicuous amount of time raising his national profile, traveling frequently to other states and engaging in national policy debates. Last week he flew into Houston, capital of the American oil business, to announce his own conservation-focused national energy plan, something that's become virtually mandatory for anyone running for President in 2008. This week he and former President Bill Clinton co-host an international climate change summit in New York.

Bloomberg himself says he's not running, has no plans to run, can't imagine running, etc., etc. But that's not the same as ruling it out entirely. He doesn't do that. But he does occasionally do things to suggest that, far from ruling out a run, he's seriously considering one. Or at least he wants the media and other speculators in the political market to think he's seriously considering a run.

How else to explain the conspicuously public dinner in Washington last week between Bloomberg and Nebraska Sen. Chuck Hagel, the Vietnam veteran and G.O.P. apostate who has come out in full opposition to President Bush and the continuation of the Iraq War? Hagel has toyed with the idea of running for the G.O.P. nomination. But he's an outsider now within the Republican family; having attacked Bush, he'd be doomed in a G.O.P. primary. Hagel's only avenue, like Bloomberg's, would be a third-party bid. It doesn't hurt that Hagel happened to make millions of his own as a cellular phone entrepreneur before he won his Senate seat. There had already been some speculation that Bloomberg and Hagel might team up. Their dinner at the Palm Restaurant, a place to be seen by media power players, was clearly meant to fuel even more.

Finally, there is a sign that one of the two major parties is worried about a possible third-party Bloomberg run. The Weekly Standard magazine, the Murdoch-owned bible of the neoconservative movement, has as its latest cover story a cartoon of a diminutive Bloomberg perched in an over-sized, throne-like chair, with the headline: "The Mystery of Michael Bloomberg: Why does a popular but mediocre mayor think he should be President?" Republicans are generally convinced that Ross Perot took a disproportionate share of his 20% of the vote in 1992 out of the hide of the incumbent Republican President, George Bush, thereby ensuring Bill Clinton's victory. Some are worried that a Bloomberg candidacy in 2008 would do the same thing: help the Democratic nominee by siphoning votes from the Republican. Some early polls suggest there is cause for such concern. Which explains why some Republicans would like to stop a Bloomberg campaign before it can begin.